Background

This is the lower reach of the larger turbulent mountain stream, Blackwood Creek in CA, USA.

Identifying reasonable modeled estimates of K600

We then ran the normal stream metabolizer model: b_Kb_oipi_tr_plrckm.stan to get modeled K600 to see if we could resolve the negative correlation between ER and K600. Priors on K600_lnQ_nodes_meanlog were set as 5 bins based on rnorm(1000, mean = logQ_mean, sd = logQ_sd) centered around the mean and logQ values 1-2 sd away from the mean.

Load different model segments with normal prior for gas exchange.

We chose segments of time where we believe GPP occurred and was greater than 0. These chunks of time are from a previous model where we binned flow and incorporated measured and estimated K600 priors from gas exchange measurements a the reach.

Metabolism with CIs for the full time series

This the raw model output. It looks okay aside from some small parts of 2023. Where GPP is in blue and ER is in orange, and the black points represent NEP.

Here is the run configuration for full model:

mm_name(type = 'bayes', pool_K600 = "binned", err_obs_iid = TRUE, err_proc_iid = TRUE, ode_method = "trapezoid", deficit_src = 'DO_mod', engine = 'stan')

Fitting priors:

K600_lnQ_nodes_meanlog = log(22) Where 16 was the mean value from observed measurements and normal pooled modeled, K600_lnQ_nodes_sdlog = 1.04 bayes_specs_new$K600_lnQ_nodes_centers <- log_bins was from prior_samples <- rnorm(1000, mean = logQ_mean, sd = logQ_sd)

Checking full model convergence

Make sure the chains converged; all r-hat values were well below 1.05 (the red line) for GPP, ER, and K600. The blue lines are the mean for each parameter.

** Some poor convergence in 2023 for K600

Looks like that weird 2023 time period corresponds to bad rhats for all parameters.

k600.rhat <- mean(na.omit(met.full$K600_daily_Rhat))
k600.rhat
## [1] 1.010588
GPP.rhat <- mean(na.omit(met.full$GPP_Rhat))
GPP.rhat
## [1] 1.002292
ER.rhat <- mean(na.omit(met.full$ER_Rhat))
ER.rhat
## [1] 1.006689

##       date                lab                 rmse              sd          
##  Min.   :2021-04-29   Length:1660        Min.   :0.0115   Min.   :0.009324  
##  1st Qu.:2022-01-23   Class :character   1st Qu.:0.0469   1st Qu.:0.287383  
##  Median :2022-09-18   Mode  :character   Median :0.0708   Median :0.422103  
##  Mean   :2022-12-01                      Mean   :0.0972   Mean   :0.402806  
##  3rd Qu.:2023-10-22                      3rd Qu.:0.1359   3rd Qu.:0.514854  
##  Max.   :2024-08-16                      Max.   :0.5736   Max.   :0.991350  
##                                          NA's   :322                        
##       min              max             range             nrmse       
##  Min.   : 5.309   Min.   : 7.071   Min.   :0.02967   Min.   :0.0108  
##  1st Qu.: 6.891   1st Qu.: 8.398   1st Qu.:0.90400   1st Qu.:0.0407  
##  Median : 7.926   Median : 9.306   Median :1.33250   Median :0.0602  
##  Mean   : 7.998   Mean   : 9.272   Mean   :1.27435   Mean   :0.0709  
##  3rd Qu.: 9.051   3rd Qu.:10.228   3rd Qu.:1.57733   3rd Qu.:0.0916  
##  Max.   :10.576   Max.   :11.698   Max.   :3.85600   Max.   :0.2196  
##                                                      NA's   :322     
##       minT             maxT            rangeT        
##  Min.   : 1.003   Min.   : 1.134   Min.   : 0.06267  
##  1st Qu.: 1.982   1st Qu.: 6.837   1st Qu.: 3.93300  
##  Median : 5.455   Median :12.025   Median : 6.25483  
##  Mean   : 6.362   Mean   :12.344   Mean   : 5.98229  
##  3rd Qu.:10.149   3rd Qu.:17.882   3rd Qu.: 8.21533  
##  Max.   :16.889   Max.   :26.203   Max.   :11.01667  
## 

Looking at the K600 and ER relationships

Here is the run configuration:

bayes_specs_new

bayes_name_new <- mm_name(type = 'bayes', pool_K600 = "normal", err_obs_iid = TRUE, err_proc_iid = TRUE, ode_method = "trapezoid", deficit_src = 'DO_mod', engine = 'stan')

Where each “lab” segment was run as individual model with the K600_lnQ_nodes_meanlog adjusted to match streamline in cms during that time.

Compared modeled and measured K600

Plots for (1) measured v modeled K600 and flow and (2) logK600 and log(flow+1).

Could be one poor measurement at the highest flow for measured gas exchange. But in general the modeled K600 does seem similar to the measured, which is kind of nice to see how robust the pool_K600 = "normal" is getting at K600.

mean_k_mod <- mean(met.clean$K600_daily_mean)
mean_k_mod
## [1] 21.11758
mean_k_measure <- mean(measured_K$K600)
mean_k_measure
## [1] 22.96813
k.q <- met.clean %>%
  left_join(mod.env.ag, by = "date") %>%
  full_join(measured_K, by = c("date", "source",
                                 "K600_daily_mean"= "K600",
                                "discharge"= "Q_cms")) %>%
  ggplot(aes(x = discharge, y = K600_daily_mean, col = source, shape=source))+
  geom_point( size = 2) +
  theme_bw()+
  #scale_x_log10(limits = c(20, 800))+
   scale_color_viridis_d(option = "viridis") 


k.q_log <- met.clean %>%
  left_join(mod.env.ag, by = "date") %>%
  full_join(measured_K, by = c("date", "source",
                                 "K600_daily_mean"= "K600",
                                "discharge"= "Q_cms")) %>%
  ggplot(aes(x = log(discharge+1), y = log(K600_daily_mean), col = source, shape=source))+
  geom_point( size = 2) +
  theme_bw()+
  #scale_x_log10(limits = c(20, 800))+
   scale_color_viridis_d(option = "viridis") 



plot_grid(k.q, k.q_log, ncol = 2)

possible_k <- (mean_k_mod+mean_k_measure)/2
possible_k
## [1] 22.04286

Full run with binned K600 informed by both measured and modeled priors

Here is the run configuration for full model:

mm_name(type = 'bayes', pool_K600 = "binned", err_obs_iid = TRUE, err_proc_iid = TRUE, ode_method = "trapezoid", deficit_src = 'DO_mod', engine = 'stan')

Quick plot of flow bins given flow range:

Where dashed vertical lines correspond to the prior locations for flow bins in bayes_specs_new$K600_lnQ_nodes_centers <- log_bins

Plots made on filtered data: met.clean filtered for days with GPP_daily_Rhat<1.05,ER_daily_Rhat<1.05, K600_daily_Rhat <1.05, as well as (GPP_97.5pct>0) and (ER_2.5pct<0).

met.clean <- met.full %>%
  filter(GPP_daily_Rhat<1.05)%>%
  filter(GPP_97.5pct>0)%>%
  filter(ER_daily_Rhat<1.05) %>%
  filter(ER_2.5pct<0)%>%
  filter(K600_daily_Rhat<1.05)

mean_k_mod <- mean(met.clean$K600_daily_mean)
mean_k_mod
## [1] 22.39667
mean_k_measure <- mean(measured_K$K600)
mean_k_measure
## [1] 22.96813
KER_cor <- round(cor(met.clean$ER_daily_mean, met.clean$K600_daily_mean, use = "complete.obs"),3)
print(KER_cor)
## [1] -0.543
KGPP_cor <-round(cor(met.clean$GPP_daily_mean, met.clean$K600_daily_mean, use = "complete.obs"),3)
print(KGPP_cor)
## [1] -0.003

The vertical dashed is the overall mean modeled K600 in the box plot.

GPP and ER

## [1] -0.704

Final thoughts.

The direction of the K600 ~ flow relationship looks more logical, where K600 increases with flow. ER and K600 are negatively correlated (-0.543), GPP and K600 are negatively correlated (-0.003). but, less strongly relative to the lower reach (GBL). The relationship between K600 and flow appears to be positive but still inflected in a strange way.

However I’m still think we should be cautious in over interpreting ER trends.

The mean modeled K600 and measured gas exchange are essentially the same 22.

Final cleaned model output:

Where GPP is in blue and ER is in orange, and the black points represent NEP.

Table summarizing excluded data from cleaned model output:

Of the 878 days with DO observations 385 days were removed.

Number of Days Explaination Percent of Days
878 Total days of DO observations 100.0
385 Total days removed 43.8
209 Days model was unable to fit 23.8
0 days where GPP rhat > 1.05 0.0
0 days where ER rhat > 1.05 0.0
0 days where K600 rhat > 1.05 0.0
176 days where modeled GPP was negative 20.0
2 days where modeled ER was positive 0.2

Table summarizing excluded data from cleaned model output:

Number of Days Explaination Percent of Days
878 Total days of DO observations 100.0
385 Total days removed 43.8
34 Days with high flow 3.9
209 Days model was unable to fit 23.8
0 days where GPP rhat > 1.05 0.0
0 days where ER rhat > 1.05 0.0
0 days where K600 rhat > 1.05 0.0
176 days where modeled GPP was negative 20.0
2 days where modeled ER was positive 0.2
354 days with clean GPP fits >= 0 42.7
658 days with clean ER fits <= 0 79.3

Session info

R version 4.4.2 (2024-10-31)

Platform: aarch64-apple-darwin20

locale: en_US.UTF-8||en_US.UTF-8||en_US.UTF-8||C||en_US.UTF-8||en_US.UTF-8

attached base packages: stats, graphics, grDevices, utils, datasets, methods and base

other attached packages: plotly(v.4.10.4), kableExtra(v.1.4.0), knitr(v.1.49), streamMetabolizer(v.0.12.1), ggpubr(v.0.6.0), readxl(v.1.4.3), zoo(v.1.8-12), cowplot(v.1.1.3), viridis(v.0.6.5), viridisLite(v.0.4.2), dataRetrieval(v.2.7.17), lubridate(v.1.9.4), forcats(v.1.0.0), stringr(v.1.5.1), dplyr(v.1.1.4), purrr(v.1.0.4), readr(v.2.1.5), tidyr(v.1.3.1), tibble(v.3.2.1), ggplot2(v.3.5.1) and tidyverse(v.2.0.0)

loaded via a namespace (and not attached): DBI(v.1.2.3), gridExtra(v.2.3), rlang(v.1.1.5), magrittr(v.2.0.3), e1071(v.1.7-16), compiler(v.4.4.2), mgcv(v.1.9-1), systemfonts(v.1.1.0), vctrs(v.0.6.5), pkgconfig(v.2.0.3), crayon(v.1.5.3), fastmap(v.1.2.0), backports(v.1.5.0), labeling(v.0.4.3), pander(v.0.6.5), deSolve(v.1.40), rmarkdown(v.2.29), tzdb(v.0.4.0), bit(v.4.5.0.1), xfun(v.0.49), cachem(v.1.1.0), jsonlite(v.1.9.1), broom(v.1.0.7), parallel(v.4.4.2), R6(v.2.6.1), bslib(v.0.8.0), stringi(v.1.8.4), car(v.3.1-3), jquerylib(v.0.1.4), cellranger(v.1.1.0), Rcpp(v.1.0.14), Matrix(v.1.7-1), splines(v.4.4.2), timechange(v.0.3.0), tidyselect(v.1.2.1), rstudioapi(v.0.17.1), abind(v.1.4-8), yaml(v.2.3.10), lattice(v.0.22-6), plyr(v.1.8.9), withr(v.3.0.2), evaluate(v.1.0.1), rLakeAnalyzer(v.1.11.4.1), sf(v.1.0-19), units(v.0.8-5), proxy(v.0.4-27), xml2(v.1.3.6), pillar(v.1.10.1), carData(v.3.0-5), KernSmooth(v.2.23-24), generics(v.0.1.3), vroom(v.1.6.5), hms(v.1.1.3), munsell(v.0.5.1), scales(v.1.3.0), class(v.7.3-22), glue(v.1.8.0), lazyeval(v.0.2.2), tools(v.4.4.2), data.table(v.1.16.4), ggsignif(v.0.6.4), LakeMetabolizer(v.1.5.5), grid(v.4.4.2), crosstalk(v.1.2.1), colorspace(v.2.1-1), nlme(v.3.1-166), Formula(v.1.2-5), cli(v.3.6.4), svglite(v.2.1.3), gtable(v.0.3.6), rstatix(v.0.7.2), sass(v.0.4.9), digest(v.0.6.37), classInt(v.0.4-11), htmlwidgets(v.1.6.4), farver(v.2.1.2), htmltools(v.0.5.8.1), lifecycle(v.1.0.4), httr(v.1.4.7), unitted(v.0.2.9) and bit64(v.4.5.2)